This invention pertains to an electrical or optical or hydraulic connector that self-aligns the plug with respect to the base, particularly for “offshore” connections, and in particular a connector in which the male plug and the receptacle base are each attached to respective support parts, which are intended to put them into alignment with one another to connect the connector. However, the alignment of these parts with one another, due to their large dimensions and the complex, limited environment in which they are used in offshore applications, is imperfect, and the alignment of the plug and the base of the connector when connecting them cannot be guaranteed, such that it is necessary to have a self-aligning mechanism for the plug and the base in order to connect them.